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Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
Stochastic sampling methods are arguably the most direct and least intrusive means of incorporating parametric uncertainty into numerical simulations of partial differential equations with random inputs. However, to achieve an overall error…
We propose a sequential minimal optimization method for quantum-classical hybrid algorithms, which converges faster, is robust against statistical error, and is hyperparameter-free. Specifically, the optimization problem of the…
We present a finite-difference integration algorithm for solution of a system of differential equations containing a diffusion equation with nonlinear terms. The approach is based on Crank-Nicolson method with predictor-corrector algorithm…
Solving partial differential equations for extremely large-scale systems within a feasible computation time serves in accelerating engineering developments. Quantum computing algorithms, particularly the Hamiltonian simulations, present a…
In quantum/classical (QM/CM) partitioning methods for multi-scale modeling, one is often forced to introduce uncontrolled phenomenological effects of the environment (CM) in the quantum (QM) domain as ab initio quantum calculations are…
The subspace method is one of the mainstream system identification method of linear systems, and its basic idea is to estimate the system parameter matrices by projecting them into a subspace related to input and output. However, most of…
This paper presents a novel randomized algorithm for robust point cloud registration without correspondences. Most existing registration approaches require a set of putative correspondences obtained by extracting invariant descriptors.…
Quantum simulation elucidates properties of quantum many-body systems by mapping its Hamiltonian to a better-controlled system. Being less stringent than a universal quantum computer, noisy small- and intermediate-scale quantum simulators…
A class of quasilinear singularly perturbed boundary value problems with a turning point of attractive type is considered. The problems are solved numerically by a finite-difference scheme on a special discretization mesh which is dense…
Recent advancements in semi-supervised deep learning have introduced effective strategies for leveraging both labeled and unlabeled data to improve classification performance. This work proposes a semi-supervised framework that utilizes a…
A rigorous mathematical framework is provided for a substructuring-based domain-decomposition approach for nonlocal problems that feature interactions between points separated by a finite distance. Here, by substructuring it is meant that a…
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
We propose a novel zeroth-order optimization algorithm based on an efficient sampling strategy. Under mild global regularity conditions on the objective function, we establish non-asymptotic convergence rates for the proposed method.…
The rapid advancements in high-dimensional statistics and machine learning have increased the use of first-order methods. Many of these methods can be regarded as instances of the proximal point algorithm. Given the importance of the…
Motivated by various applications, unbounded Hamiltonian simulation has recently garnered great attention. Quantum Magnus algorithms, designed to achieve commutator scaling for time-dependent Hamiltonian simulation, have been found to be…
We propose an efficient residual minimization technique for the nonlinear model-order reduction of parameterized hyperbolic partial differential equations. Our nonlinear approximation space is a span of snapshots evaluated on a shifted…
First quantized, grid-based methods for chemistry modelling are a natural and elegant fit for quantum computers. However, it is infeasible to use today's quantum prototypes to explore the power of this approach, because it requires a…
We develop a set of methods to improve on the results of self-supervised learning using context. We start with a baseline of patch based arrangement context learning and go from there. Our methods address some overt problems such as…
We prove first-order convergence of the semi-explicit Euler scheme combined with a finite element discretization in space for elliptic-parabolic problems which are weakly coupled. This setting includes poroelasticity, thermoelasticity, as…